Introducing Multiplication of Fractions Based on Math Solutions

Introducing Multiplication of Fractions Based on Math Solutions by Marilyn Burns Online Newsletter Issue Number 12, Winter 2003 -2004

What is multiplication? • The same as repeated addition when you add the same number again and again • Times means “groups of” • Can be shown as a rectangle • Can reverse the order of the factors and the product stays the same • When multiplying two numbers, the product is larger than the factors, unless one of the factors is a zero or a fraction ***Do you think all of these rules are true when you are multiplying fractions?

How do we multiply 4 x ½? • How could you solve this problem using repeated addition? • Student examples:

4 x 1/2 • How could we say this problem if “times means groups of? ”

4 x 1/2 • How could you show this multiplication problem using rectangles?

4 x 1/2 • How can we show that the order of the factors can be reversed and the product stays the same? Student Examples:

4 x 1/2 • When you multiply two numbers, the product is larger than the factors unless one of the factors is one or zero • Examples: 6 x 7 = 8 x 1 = 9 x 0 = • Is this true with fractions? • How should the rule be rewritten?

Summary (Respond to the following questions in your math journal or on paper. ) • Show and explain how 5 x 1/7 and 1/7 X 5 are similar. • Apply another rule that you learned today to the problem 3 x 1/5! • Tell how multiplication of whole numbers is different from multiplication of fractions.